Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

Test-retest reliability of structural brain networks from diffusion MRI

Structural brain networks constructed from diffusion MRI (dMRI) and tractography have been demonstrated in healthy volunteers and more recently in various disorders affecting brain connectivity. However, few studies have addressed the reproducibility of the resulting networks. We measured the test–retest properties of such networks by varying several factors affecting network construction using ten healthy volunteers who underwent a dMRI protocol at 1.5 T on two separate occasions. Each T1-weighted brain was parcellated into 84 regions-of-interest and network connections were identified using dMRI and two alternative tractography algorithms, two alternative seeding strategies, a white matter waypoint constraint and three alternative network weightings. In each case, four common graph-theoretic measures were obtained. Network properties were assessed both node-wise and per network in terms of the intraclass correlation coefficient (ICC) and by comparing within- and between-subject differences. Our findings suggest that test–retest performance was improved when: 1) seeding from white matter, rather than grey; and 2) using probabilistic tractography with a two-fibre model and sufficient streamlines, rather than deterministic tensor tractography. In terms of network weighting, a measure of streamline density produced better test–retest performance than tract-averaged diffusion anisotropy, although it remains unclear which is a more accurate representation of the underlying connectivity. For the best performing configuration, the global within-subject differences were between 3.2% and 11.9% with ICCs between 0.62 and 0.76. The mean nodal within-subject differences were between 5.2% and 24.2% with mean ICCs between 0.46 and 0.62. For 83.3% (70/84) of nodes, the within-subject differences were smaller than between-subject differences. Overall, these findings suggest that whilst current techniques produce networks capable of characterising the genuine between-subject differences in connectivity, future work must be undertaken to improve network reliability

Introducing axonal myelination in connectomics: a preliminary analysis of g-ratio distribution in healthy subjects

Microstructural imaging and connectomics are two research areas that hold great potential for investigating brain structure and function. Combining these two approaches can lead to a better and more complete characterization of the brain as a network. The aim of this work is characterizing the connectome from a novel perspective using the myelination measure given by the g-ratio. The g-ratio is the ratio of the inner to the outer diameters of a myelinated axon, whose aggregated value can now be estimated in vivo using MRI. In two different datasets of healthy subjects, we reconstructed the structural connectome and then used the g-ratio estimated from diffusion and magnetization transfer data to characterise the network structure. Significant characteristics of g-ratio weighted graphs emerged. First, the g-ratio distribution across the edges of the graph did not show the power-law distribution observed using the number of streamlines as a weight. Second, connections involving regions related to motor and sensory functions were the highest in myelin content. We also observed significant differences in terms of the hub structure and the rich-club organization suggesting that connections involving hub regions present higher myelination than peripheral connections. Taken together, these findings offer a characterization of g-ratio distribution across the connectome in healthy subjects and lay the foundations for further investigating plasticity and pathology using a similar approach

The white matter connectome as an individualized biomarker of language impairment in temporal lobe epilepsy.

ObjectiveThe distributed white matter network underlying language leads to difficulties in extracting clinically meaningful summaries of neural alterations leading to language impairment. Here we determine the predictive ability of the structural connectome (SC), compared with global measures of white matter tract microstructure and clinical data, to discriminate language impaired patients with temporal lobe epilepsy (TLE) from TLE patients without language impairment.MethodsT1- and diffusion-MRI, clinical variables (CVs), and neuropsychological measures of naming and verbal fluency were available for 82 TLE patients. Prediction of language impairment was performed using a robust tree-based classifier (XGBoost) for three models: (1) a CV-model which included demographic and epilepsy-related clinical features, (2) an atlas-based tract-model, including four frontotemporal white matter association tracts implicated in language (i.e., the bilateral arcuate fasciculus, inferior frontal occipital fasciculus, inferior longitudinal fasciculus, and uncinate fasciculus), and (3) a SC-model based on diffusion MRI. For the association tracts, mean fractional anisotropy was calculated as a measure of white matter microstructure for each tract using a diffusion tensor atlas (i.e., AtlasTrack). The SC-model used measurement of cortical-cortical connections arising from a temporal lobe subnetwork derived using probabilistic tractography. Dimensionality reduction of the SC was performed with principal components analysis (PCA). Each model was trained on 49 patients from one epilepsy center and tested on 33 patients from a different center (i.e., an independent dataset). Randomization was performed to test the stability of the results.ResultsThe SC-model yielded a greater area under the curve (AUC; .73) and accuracy (79%) compared to both the tract-model (AUC: .54, p < .001; accuracy: 70%, p < .001) and the CV-model (AUC: .59, p < .001; accuracy: 64%, p < .001). Within the SC-model, lateral temporal connections had the highest importance to model performance, including connections similar to language association tracts such as links between the superior temporal gyrus to pars opercularis. However, in addition to these connections many additional connections that were widely distributed, bilateral and interhemispheric in nature were identified as contributing to SC-model performance.ConclusionThe SC revealed a white matter network contributing to language impairment that was widely distributed, bilateral, and lateral temporal in nature. The distributed network underlying language may be why the SC-model has an advantage in identifying sub-components of the complex fiber networks most relevant for aspects of language performance

Measuring cortical connectivity in Alzheimer's disease as a brain neural network pathology: Toward clinical applications

Objectives: The objective was to review the literature on diffusion tensor imaging as well as resting-state functional magnetic resonance imaging and electroencephalography (EEG) to unveil neuroanatomical and neurophysiological substrates of Alzheimer’s disease (AD) as a brain neural network pathology affecting structural and functional cortical connectivity underlying human cognition. Methods: We reviewed papers registered in PubMed and other scientific repositories on the use of these techniques in amnesic mild cognitive impairment (MCI) and clinically mild AD dementia patients compared to cognitively intact elderly individuals (Controls). Results: Hundreds of peer-reviewed (cross-sectional and longitudinal) papers have shown in patients with MCI and mild AD compared to Controls (1) impairment of callosal (splenium), thalamic, and anterior–posterior white matter bundles; (2) reduced correlation of resting state blood oxygen level-dependent activity across several intrinsic brain circuits including default mode and attention-related networks; and (3) abnormal power and functional coupling of resting state cortical EEG rhythms. Clinical applications of these measures are still limited. Conclusions: Structural and functional (in vivo) cortical connectivity measures represent a reliable marker of cerebral reserve capacity and should be used to predict and monitor the evolution of AD and its relative impact on cognitive domains in pre-clinical, prodromal, and dementia stages of AD. (JINS, 2016, 22, 138–163

Altered Anatomical Network in Early Blindness Revealed by Diffusion Tensor Tractography

The topological architecture of the cerebral anatomical network reflects the structural organization of the human brain. Recently, topological measures based on graph theory have provided new approaches for quantifying large-scale anatomical networks. Diffusion MRI studies have revealed the efficient small-world properties and modular structure of the anatomical network in normal subjects. However, no previous study has used diffusion MRI to reveal changes in the brain anatomical network in early blindness. Here, we utilized diffusion tensor imaging to construct binary anatomical networks for 17 early blind subjects and 17 age- and gender-matched sighted controls. We established the existence of structural connections between any pair of the 90 cortical and sub-cortical regions using deterministic tractography. Compared with controls, early blind subjects showed a decreased degree of connectivity, a reduced global efficiency, and an increased characteristic path length in their brain anatomical network, especially in the visual cortex. Moreover, we revealed some regions with motor or somatosensory function have increased connections with other brain regions in the early blind, which suggested experience-dependent compensatory plasticity. This study is the first to show alterations in the topological properties of the anatomical network in early blindness. From the results, we suggest that analyzing the brain's anatomical network obtained using diffusion MRI data provides new insights into the understanding of the brain's re-organization in the specific population with early visual deprivation